Answer
$P$-value $\gt α$: null hypotheses is not rejected.
There is not significant evidence to conclude that the proportion of Americans who work at home has increased since 2009.
Work Step by Step
$H_0:~p=0.021$ versus $H_1:~p\gt0.021$
$np(1-p)=150\times0.021(1-0.021)=3.08385\lt10$
Test hypotheses with a small sample size:
$P$-value $=P(X\geq6)=1-P(X\lt6)=1-P(X\leq5)$
In order to find $P(X\leq5)$ use Excel: "=BINOMDIST(5;150;0.021;TRUE)"
$P$-value $=1-P(X\leq5)=1-0.9024=0.0976$
Since $P$-value $\gt α$, we do not reject the null hypotheses.
